Type lcalc.[tab] for a list of useful commands that
are implemented using the command line interface, but return
objects that make sense in Sage. For each command the possible
inputs for the L-function are:

Return the imaginary parts of the first \(n\) nontrivial
zeros of the \(L\)-function in the upper half plane, as
32-bit reals.

INPUT:

n - integer

L - defines \(L\)-function (default:
Riemann zeta function)

This function also checks the Riemann Hypothesis and makes sure no
zeros are missed. This means it looks for several dozen zeros to
make sure none have been missed before outputting any zeros at all,
so takes longer than
self.zeros_of_zeta_in_interval(...).

Return the imaginary parts of (most of) the nontrivial zeros of the
\(L\)-function on the line \(\Re(s)=1/2\) with positive
imaginary part between \(x\) and \(y\), along with a
technical quantity for each.

INPUT:

x,y,stepsize - positive floating point
numbers

L - defines \(L\)-function (default:
Riemann zeta function)

OUTPUT: list of pairs (zero, S(T)).

Rubinstein writes: The first column outputs the imaginary part of
the zero, the second column a quantity related to \(S(T)\)
(it increases roughly by 2 whenever a sign change, i.e. pair of
zeros, is missed). Higher up the critical strip you should use a
smaller stepsize so as not to miss zeros.